The longitudinal variational autoencoder (L-VAE) [1]} is an extension of the VAE that is tailored to longitudinal data.
It can model both time-varying shared as well as random effects through the use of a multi-output additive GP prior.
However, the model makes the strong assumption that the observed data is normally distributed. On the other hand, the work by [2]} proposed a general extension to the VAE that can handle both heterogeneous and missing data; however, it is not capable of longitudinal analysis.
In this work, we build upon these ideas and propose a model that probabilistically encodes temporal and longitudinal measurements that may comprise of discrete as well as continuous (i.e.,  heterogeneous) data onto a low-dimensional homogeneous latent space while handling missing values that are missing completely at random (MCAR).
The structured low-dimensional latent space dynamics are modelled using a multi-output additive GP prior as in [1]}, and the heterogeneous data can be reconstructed (or decoded) using a deep neural network based decoder.
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